Please. It is not okay to keep supporting an idea until the minute the counter to that idea becomes available, when you'll be eager to benefit from the "counter" solution.
It was not okay for Ayn Rand to be a libertarian all her life, only to start collecting welfare checks at the end of her life when she went broke.
I'm not even getting into the practical aspects of how badly the pro-aging trance is affecting the funding problem.
However, I think this thought experiment can bring them to understand that their own beliefs are temporary. If there was a popular movie that followed the plot of how the cure of aging was slowly accepted in society, for example.
Just a short story might be a start.
I think the problem is not that people "support" the idea, but that they are not properly aware of the alternative.
Ayn Rand didn't change her views. Period. She was just blatantly self-serving.
Most people do not support some Moral Ideal of Death. They just consider the actual dying bit inevitable. This is why they will change their minds once you show, in the real world, that it's changeable.
You're assuming that the treatment will be within reach for everybody. What if only rich people will be able to afford it?
It might be seen as even less important than distributing food to the starving, and medicine to the sick, of which there is still not enough going on.
But there is at least one other pathway. As an AGI researcher, I believe that artificial intelligence will solve the problem for us, and, all other things being equal, the cure will be made available everywhere, at the same time.
My own research makes me believe that we are not very far from that outcome.
I do not see that happening in the long-term. Maybe a few fringe sects, but never the majority.
Instead, as soon as some people use such treatment, most everyone else will as well.
What this conjecture tells me, is that this "culture" is probably just based on the belief that anyone who refuses to accept aging, must be a fool.
If however a cure is demonstrated, this belief will be disproven, and people will quite immediately embrace longevity.
Or.. do you expect otherwise?